Short Answer TypeA proton and an α-particle have the same de-Broglie wavelength. Determine the ratio of (i) their accelerating potentials (ii) their speeds.
Show that the radius of the orbit in hydrogen atom varies as , where n is the principal quantum number of the atom.
Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f?
(i) A giant refracting telescope has an objective lens of focal length 15 m. If an eye piece of focal length 1.0 cm is used, what is the angular magnification of the telescope?
(ii) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens ? The diameter of the moon is 3.48 × 106 m and the radius of lunar orbit is 3.8 × 108 m.Write Einstein’s photoelectric equation and mention which important features in photoelectric effect can be explained with the help of this equation. The maximum kinetic energy of the photoelectrons gets doubled when the wavelength of light incident on the surface changes from 
to 
. Derive the expressions for the threshold wavelength 
and work function for the metal surface.
Einstein’s photoelectric equation is given as: 
where, h
is the energy of the photon,
, is the work function of the metal,
is the maximum kinetic energy of the emitted photoelectron.
Maximum kinetic energy is given by,
;
where 
is the threshold frequency of the metal surface.
Features of the equation of photo-electric effect are:
a) When a photon of suitable radiation falls on the metal surface, a photoelectron is ejected. If the intensity of the light is increased number of photons incident on the metal surface increases and hence, the number of photo-electrons ejected also increases. This implies photo current is proportional to intensity and radiation.
b) If the frequency is less than the threshold frequency, i.e., the photoelectric emission does not take place for incident radiation.
c) When the frequency of the incident light is greater than the threshold frequency, the maximum K.E increases. This implies maximum K.E of photoelectrons depends upon the frequency of incident light.
Einstein’s equation corresponding to wavelength 
Einstein’s equation corresponding to wavelength 
is, 
From equation (1) and (2), we have
where 
is the threshold wavelength.
In the study of Geiger-Marsdon experiment on scattering of α particles by a thin foil of gold, draw the trajectory of -particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study. From the relation R = Ro A1/3 where Ro is constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A.
Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction:
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